Fuzzy Sets and Formal Logics

The paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics. Our focus is on the historical side of these developments. © 2015 Elsevier B.V. All rights reserved.partial support by the Spanish projects EdeTRI (TIN2012-39348- C02-01) and 2014 SGR 118.Peer reviewe

The syntactic derivations of interrogative verbs in Amis and Kavalan

Interrogative words that denote ‘what’, ‘how’, ‘where’, and ‘how many’ in Amis and Kavalan have the same morphosyntactic distribution as verbs. The present paper argues that their use as verbs is not due to unconstrained lexical idiosyncrasies, but exhibits consistent syntactic and semantic patterns. Their grammatical properties and restrictions follow from the interaction of the following factors: the inherent semantics of interrogative words, the available interpretation of the question where they occur, the verbal structures of the voice markers, and the syntactic principles and constraints like the Head Movement Constraint or the Transparence Condition. The syntactic analysis advocated in this paper can extend to other atypical non-interrogative verbs in the two languages and makes falsifiable predictions about what interrogative words can and cannot be used as verbs

Compositional lexical networks: a case study of the English spatial adjectives

Most words cannot be given a single precise definition, but instead consist of multiple senses related to each other like members of a family. In cognitive approaches to semantics, this kind of category is described by a lexical, a diagram in which nodes represent senses and arrows represent sense connections. However, lexical network theory is not compositional: it does not explain how lexical networks are combined together to yield the meanings of phrases and sentences. The aim of this thesis is to develop lexical network theory in a formal, compositional setting. I argue that a traditional approach to formal semantics based on the simply-typed lambda calculus is not rich enough to implement lexical networks because it is unable to type the arrows which link word senses together. Instead, I propose replacing simple type theory with Martin-Löf Dependent Type Theory, and show how this allows for a fully compositional implementation of lexical networks. The resulting theory is applied to the description of the English spatial adjectives - high, low, tall, long, short, deep, shallow, thick and thin. These adjectives are an ideal starting point for studying the interaction between lexical and compositional semantics, since they have been studied extensively from both points of view. I illustrate how a compositional theory of lexical networks can provide an interface by which the insights of cognitive semantics can be imported into formal semantics, and vice versa

Typology and Evolution of Cardinal Numeral-Noun Constructions

The principles of economy and distinctness in language seem to be key selection pressures for language evolution. Accordingly, to express the exact number of things, humans might be expected to use cardinal numeral-noun constructions (CNNCs) consisting of just two constituents, namely a noun (N) representing quantified things and a cardinal numeral (NUM) representing the number of the quantified things (for example, English three sheep). However, the structural patterns of CNNCs used in a number of languages spoken today are not that simple, and have seemingly redundant constituents, typically non-singular markers (NSG) and numeral classifiers (CLF). CNNCs observed in the world's languages also appear to show a diversity of structural patterns despite the fact that simple structures like English three sheep seem very practical. This observation brings up two related major goals of this thesis. The first is to reveal structural types of cardinal numeral-noun constructions of singularity (CNNCsg) and cardinal numeral-noun constructions of non-singularity (CNNCnsg)- The other major goal is to hypothesize a possible evolutionary scenario for CNNCs since their emergence till the modern era.This thesis approaches these two issues by exploring CNNCs in 241 languages representing 101 language groups (i.e. language families, language isolates and pidgins and Creoles) across the globe through reference grammars to ensure the greatest range of possible attested structural patterns of CNNCs. This cross-linguistic survey demonstrates that, with regard to CNNCsg, the world's languages are divided into two major types, namely {N,NUM} and {N,NUM,CLF} with relatively few other possibilities. In relation to CNNCnsg, the world's languages are divided into four major types, namely {N,NUM}, {N,NUM,NSG}, {N,NUM,CLF} and a mixture of {N,NUM} and {N,NUM,NSG} with some other less common possibilities. The historical origins of these structural types are then investigated, using evidence from old written records together with theoretical approaches, especially grammaticalization. Finally, it is found that the various structural patterns of CNNCs discovered can be considered in the light of a hypothetical evolutionary ladder. Hence, with cross-linguistic comparison integrated with diachronic approaches, hypothesized evolutionary trajectories of CNNCs are postulated. It is conjectured that the construction consisting of a noun plus a word with a numerical interpretation such as the words meaning 'alone' or 'company' may represent a possible initial stage of CNNCs. From that stage onwards, CNNCs have split into many types over time. The development is reversible in terms of structural complexity, and idiosyncratic in some cases. Besides, the contributory factors in the development of CNNCs involve a quantifying function, a non-quantifying function, and a mixture of both.Based on the study of evolution of CNNCs, this thesis also discusses the nature of language by comparing language change with biological evolution in some major aspects. The comparison suggests that language is strikingly similar to biological organisms in general, perhaps rather than to other cultural artefacts. Overall, this thesis contributes to current studies of the complexity and diversity of human language(s

Fuzzy Natural Logic in IFSA-EUSFLAT 2021

The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications

Adjectival forms in Middle English: syntactic and semantic implications.

[Abstract] Our main purpose in this paper is to look into the place of adjectives in a particular period in the history of English as regards their position in the Noun Phrase and whether such position may somehow alter the meaning of the adjective and of the NP itself. To this end, only adjectives in an attributive function both as premodifiers or postmodifiers of the head will be considered. In section 1 we will briefly attempt to draw a line between the class “adjective” and other morphological classes considering different viewpoints. Section 2 will be devoted to the consideration of word-order as one of the factors characterising adjectives inside the NP and how their position may alter the meaning of the whole phrase. The next step in our research will be embodied in section 3 where we will present the corpus material for our study taken from the Middle English part of the Helsinki Corpus of English Texts and section 4 will provide the analysis of the data obtained from our evidence. Section 5 will finally supply our conclusions. We will attempt —if possible— to find an explanation grounded on syntactic and semantic criteria for the different shades of meaning found to depend on position